QUESTION: A vertical dial's gnomon traces an inverted U in the summer months, and of course a U in the winter ones. They are the hyperbolic lines. BUT, in the summer it is an inverted U, yet for a shepherd's dial, the lines are always U shaped.

The vertical dial nodus shadow traces are hour angle based, but do contain azimuth and altitude data. The shepherd's dial is altitude only and the gnomon ALWAYS points to the sun, not so for a vertical dial. If you consider the fact that the altitude shown on a vertical dial is skewed by the concurrent azimuth, then this begins to make sense. In fact, if you measured the altitude from the nodus of a vertical dial, you would find that the altitude actually peaks at solar noon and either side, the altitude is actually less. It only looks steeper because of the U curves, and they are skewed by azimuth. Have some fun and measure the angles yourself!

QUESTION: The equatorial, the armillary, and the horizontal dial all have 6 o'clock (am or pm) at 90 degrees to the noon line (for non longitude adjusted dials). So, why does the azimuth dial not have 6 o'clock at 90 degrees to noon?

The azimuth dial is horizontal and thus is a projection of the equatorial dial, and that skews the lines. On the equinox, yes 6am and 6pm are perpendicular to noon for the azimuth dial. However, the summer solstice ray from the sun to the gnomon will hit the equatorial dial at 90 degrees to noon, however if the ray continues down to the horizontal azimuth dial, it displaces south. So, for horizontal azimuth dials, 6 o'clock will be north or south of the 90 line from noon. But you say, how is it the horizontal hour angle dial has 6 o'clock at 90 degrees? the answer is because of the sloping gnomon. In fact the tip of the gnomon (nodus) on a horizontal dial is north of the 6 o'clock lines at all times of the year (for the northern hemisphere).

QUESTION: Why do the print runs appear more frequently than for other books? Why did the second edition come out so soon after the first edition?

The first edition lost the last two weeks of editing, those changes are available in all-updates.pdf and anyone who purchased the first edition before 4/9/05 got a free second edition. That was why the second edition came out so quickly. The print runs were kept small so that the few remaining clarifications needed, based on feedback, could get into the system more quickly. Feedback has been very good, and all feedback has been considered. The second edition has had very few "opportunities for improvement", and they are in reference-updates.pdf here. FEEDBACK is extremely welcome, and new material is posted on this web site. For example the Durer chapter, the Software chapter, the Stained Glass chapter, the Declination line chapter, etc, have all been placed on this web site, and the best place to find them is on the main web page here. Continuous feedback improves the product, and because the updates are made available, and because new material is posted here, your investment in the book is not only protected, it grows. The moral of the story is ~ please buy the book now! You can see the options to buy the book on the PayPal page. The book sells for less than you can copy it! And the book specifically allow limited copying with no charge, the sole requirement is that you notify me at "illustratingshadows at yahoo.com" and all feedback should be sent there also. All feedback is considered, and most causes an immediate change, some causes a change but not where you suggested it, and very very little results in no change. And I respond to all feedback. Thanks.

ANSWER: The padded envelope costs $0.70, hence the difference. And that ignores gas, and so on. S&H means shipping and handling, and handling can be many things. I eat some postage, and sales tax.

QUESTION: Why isn't sunset the same as sunrise at the equinoxes?

ANSWER: When the declination is 0 then sunset = sunrise provided two other things are 0 also! Namely the EOT and the locations longitude - locations reference longitude. Sunset - 12 noon + (12 noon - sunrise), then EOT is applied, then the longitude correction. If you set the EOT to 0 in the spreadsheet, if you set the longitude reference to equal the locations longitude then you will see sunset - sunrise where the declination is zero.

QUESTION: On page 125 there is a winged azimuth dial. There is no way the hour points can ever be lined up with anywhere, not dial center, not the nodus base, nowhere. Since a normal hour angle dial with a right angled gnomon by definition provides azimuth by the nodus to nodus base line, is not the winged azimuth sun dial incorrect?

ANSWER: Looks that way doesn't it! But no. Azimuth dials do not have hour lines, and their hour points are not fixed points, they merely form an hour line for one hour on one date. If you drew a horizontal dial with a dial center, and used the angles of lines from the nodus base to the hour point, then those lines would intersect the real single hour line. And those intersection points would be declination or calendar points.

QUESTION: Why do the declination tables you have in the appendix differ from some other authors?

ANSWER: Look at table A2.11 September 1. The table shows a declination of 8.4 degrees, and in the second edition it is 8.6 degrees. Waugh page 206 shows 8.5 degrees, Mayall on page 133 shows 8.3 to 8.4 degrees. Formulae such as these use approximations and series, and some use the calendar julian date, some use a true astronomical julian data. Approximations for the leap year, methods used by differing spreadsheets, and rounding due to precision all account for some variation. The question is best framed as "are the differences significant when using the method you will use when laying out a dial?" You may check online almanacs, and you may download the spreadsheet for A2.11, or any other spreadsheet here if you wish, and then refine them. Similarly, I have three different formulae for the equation of time that use the normal yearly leap cycle, and two that use the astronomical julian day that accounts for an annual drifting. Not one produces a result that always matches other tabulations. The most accurate would consider the astronomical method, and that changes by the year, which explains other discrepancies. In the times of Chaucer, their EOT was different measurable from ours in the 21st century!

QUESTION: Why is your book's polar dial formula different from some other authors?

ANSWER: This book uses noon as the basis for the polar dial and 6am or 6pm as the basis for meridian (east or west) facing dials. Those points exist on the dial, so it made sense. It also means that references in the formula are from the sub-style in all cases, and not from the sub-style in one case, and infinity in the other. Not inconsistent, merely different. The end result is that this book's hour lines match those of all other authors.

FAQs

QUESTION: Equatorial, equinoctial or armillary, meridian or vertical? What is what, different people use the same terms for different things.

Armillary often refers to the full armillary spheres, actually bracelets, as worn on an arm, hence the word. Equatorial dials are ones whose plane is parallel to the equator. Many people say that the armillary plane is parallel to the equator. Others, like me, say that the armillary dial plate is perpendicular to the equator, since that is where the numbers on the dial plate lie, thus an armillary has arm bands that parallel the ppolar axis. The equatorial dial truly has a dial plate with numbers on it paralleling the equatorial plane. The equatorial dial is sometimes called an equinoctial since it bifurcates at the equinoxes, summer shadows are on the sky side, winter shadows on the earth side.

Meridian dials are dials whose plate lies in the meridian, namely parallel to the polar axis, like the true east and true west facing vertical dials. Some people call vertical north or south dials meridian dials since their style lies in the meridian. All styles lie in the meridian for hour angle dials.

The real point is to know what you are looking at. Gnomonics is filled with ambiguous terms, declination can mean (1) wall declination from true north or south, (2) the suns declination or angle of rays north or south of the equator, or (3) magnetic variation whereby that variation acuses true and magnetic north not to coincide.

QUESTION: Why does EOT sign differ from the EOT sign (+ vs -) in the nautical and other almanacs.There are two conventions used. One is used by sundial people, and the sign it added to the local apparent time, and the other is for astronomical folk, and they add their EOT to the time to locate the sun. Hence, a sundial user will have a "+", where the astronomer would have a "-", and vice versa. It is a matter of convention. Another example for confusion, albeit unrelated, is the use of the word declination which has three meanings for the sundial community. In particular, magnetic declination in the sundial community means magnetic variation in the navigation arena.

WHAT IS THE BOTTOM LINE FOR CALENDAR CURVES?

Declination lines or curves are always symmetrical about the SD (style distance line). They only look non symmetrical on dials such as the east and west decliners because about half of the dial is always missing. IE an east dial has no afternoon hours, a west dial has no morning hours. Thus a declination set of curves for lat 32 is the same as lat -32. In other words, the sign can be ignored on SH, since SH is always above the dial plate, and SH (style height) is the latitude for declination or calendar curves.

Not true for SD, style distance, because it may be either side of the vertical. The use of SH for the apparent latitude for the calendar curves is important because...

1. A dial plate is merely a presentation device for shadows, and thus is a geometrical mapping of the sun's circular movement to a plate that displays it.2. This shows further an important point, namely that with correct alignment, altitude and azimuth are portable, an issue I discuss towards the end of book 2. There is argument that this is not the case, however, clearly it is portable provided certain constraints exist.3. That is why I have a calendar curve generator in DeltaCAD that is separate from the dials, it further emphasises the relationship of calendar or declination lines or curves and SH.

QUESTION: Italian hour lines are clearly local apparent time. So why make a longitude correction on a dial with Italian hour lines?

If the dial plate is not longitude corrected then the winter and summer solstice indicated times on the dial plate are used for the anchor points of the Italian hour lines.

But, if the dial plate is longitude adjusted then that would no longer be true because the displayed or indicated times would no longer be LAT (local apparent time). So, if the dial plate has been longitude corrected then the Italian hour line anchor points should also be longitude adjusted so that the end result is that the Italian hour lines are where they would be on the dial plate were no longitude correction applied at all. See the case study of the polar dial for an example.

QUESTION: What happened to Illustrating Shadows and its sequel, Illustrating More Shadows?

ANSWER: Illustrating More Shadows was the sequel to Illustrating Shadows. The first book dealt with a lot of theory and small dials, the sequel dealt with more dial types and outdoor and large dials. There was some duplication. Rather than do a 4th edition of Illustrating Shadows and a 2nd edition of Illustrating More Shadows I decided to merge both books and remove the appendices to a separate book. Thus, Illustrating Time's Shadow is in reality the 4th edition of the first book as well as the second edition of its sequel. Illustrating Time's Shadow thus replaces both original books, deletes duplicate as well as infrequent or overly complex material, adds new material, and rearranges the sequence for easier flow. It has a minimum appendix, and the full appendices of 150 pages is free to download, or you can purchase it in printed form. Thus what I have for sale is simplified. The big book Illustrating Time's Shadow, with a NASS/BSS discount and media mail, priority mail, or overseas from USA airmail shipping options. The appendices are one price (which is my cost) but the same shipping options. The CD and the online purchase, as well as the CD with the book, all have the original current books Illustrating Shaodws and Illustrating More Shadows. You cannot lose.

QUESTION: Why is your book's vertical decliner and ceiling dial formula different from some other authors?

ANSWER: I derived my formulae from scratch using the minimum of special trigonometric tricks (identities) so anyone could follow their derivation. Similarly with my planispheric astrolabe. The formulae have been cross checked against the more common formulae and they match.

QUESTION: Why is the noon line not vertical on my vertical dial. The noon line is vertical for vertical dials that are at the longitude of the legal meridian. As you move off the legal meridian, the hour line will no longer be vertical but offset. The offset makes a noon line that is actually before or after noon by an amount of minutes equal to the difference between your longitude and the legal meridian times 4. I am at about long 108, the legal meridian is at 105, so the is about a 3 degree difference or a 12 minute difference. So my dials have a vertical line to the west, showing noon (or any other hour for that matter), 12 minutes early. Ditto for vertical decliners. The books have "rules of thumb" in the indices which have such things pointed out.

United Kingdom established sundials in their school syllabus: check both here and here

QUESTION: Why does the sunrise/set time in the PDA XLS (Docs To Go) disagree with the standalone almanac PRC for the PDA?The spreadsheet corrects for longitude and EOT, the standalone program shows the net correction and leaves it to you to do the math. It does this because it also shows altitude and azimuths which are not corrected either.

QUESTION: Why are DL and SD not the same angle?SD is the angle by which the sub style is rotated for a vertical decliner, and as such, it is an hour LINE angle, DL is the angle on a surrogate equatorial dial that produces the hour line angle of DL.

QUESTION: Why have a Dial FURNITURE set of macros when they are already in the MAIN set of DeltaCAD macros? Nov 26, 2013Several reasons. One was to have a small collection available for just dial furniture; the Supplemental Shadows book has a furniture chapter, and refers to the furniture macros alone. Another reason goes back to some versions of DeltaCAD could not handle large macros, so I extracted the furniture code from them to make the main macros smaller and created the furniture macro set. DeltaCAD since addressed he macro size issue, so I later put the furniture macros back into the main ones, while retaining the original furniture macros.

QUESTION: Why do you not discuss "Powerdraw" software, it is programmable? April 13, 2016It is discussed in Programming Shadows, just not in the other books. The Powerdraw software is programmable. However, the documentation is marginal at best. Nowhere could I find, and I did experiment, trigonometric functions. Sundial programming requires at a minimum SIN COS, TAN, and preferably ATAN. In spite of that I wrote my own sin, cos, and tan, and asn, acs, and atan, and thus have Powerdraw macros here for the hDial, vDial, and vDec.

QUESTION: Shadow rotation on vertical dials, page 157 of Illustrating Time's Shadow, clarify what is clockwise, and what is counter clockwise? July 16, 2013There are several points on page 157. One is for north vertical dials in the northern hemisphere (top part of the big box), one is for south vertical dials in the northern hemisphere, and how each shadow rotates. The smaller boxes are gnomon offset WHEN the dial is offset from true north or south (as in a vertical declining dial). Details are here.....

QUESTION: Why does the index page and almanac page of the master spreadsheet have different numbers for the locations EOT corrected for EOT, when compared to the EOTandLONG worksheet? September 11, 2013The first two use a generic EOT from a simple formula, the EOTandLONG uses the average over 4 years of the astronomically accurate EOT. This spreadsheet and the big book all emphasise that there are several different EOT formulae out there, and they differ slightly.Changed Sept 13, 2013 so more tables use the 4 year average astronomical EOT which averages 2010 to 2013

QUESTION: Why do you not use spherical trig for formulae proofs, it is more generalised? April 13, 2016A key founding value for the entire Illustrating Shadows collection was that it should be understandable to a high school student who graduated and liked math. That means the main book, appendices, supplemental and programming books, and software.